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Groups of order automorphisms of ordered sets

Published online by Cambridge University Press:  26 February 2010

P. M. Cohn
P. M. Cohn
Affiliation:
The University, Manchester 13.
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Extract

Let S be an ordered set, i.e. a set with a transitive irreflexive binary relation “<” such that, for any a, bεS, either a = b or a < b or b < a. By an order automorphism of S we mean a one-one mapping α of S onto itself such that

Type
Research Article
Information
Mathematika , Volume 4 , Issue 1 , June 1957 , pp. 41 - 50
Copyright
Copyright © University College London 1957

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References

1.Birkhoff, G., Lattice theory (2nd ed., New York, 1948).Google Scholar
2.Iwasawa, K., “On linearly ordered groups”, J. Math. Soc. Japan, 1 (1948), 1–9.CrossRefGoogle Scholar
3.Neumann, B. H., “On ordered groups”, American J. Math., 71 (1949), 1–18.CrossRefGoogle Scholar